We present images and high-resolution spectra of the planetary nebulae IC 2553 and NGC 5882. Spatiokinematic modeling of the nebulae shows that they are composed of a markedly elongated inner shell and of a less aspherical outer shell expanding at a considerably higher velocity than the inner one. Embedded in the outer shells of both nebulae are found several low-ionization knots. In IC 2553, the knots show a point-symmetric distribution with respect to the central star: one possible explanation for their formation is that they are the survivors of preexisting point-symmetric condensations in the asymptotic giant branch wind, a fact that would imply a quite peculiar mass-loss geometry from the giant progenitor. In the case of NGC 5882, the lack of symmetry in the distribution of the observed low-ionization structures makes it possible that they are the result of in situ instabilities. Based on observations obtained at the 3.5 m New Technology Telescope (NTT) of the European Southern Observatory and with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA for NASA under contract NAS5-26555.